Dynamic Modeling of an Underground Gas Storage Facility, History Matching and Prediction

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DYNAMIC MODELING OF AN

UNDERGROUND GAS STORAGE FACILITY

HISTORY MATCHING AND PREDICTION

by

Karakoz Kozhakhmetova

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A thesis submitted to the Department of Mineral Resources and Petroleum Engineering of the Mining University of Leoben in partial fulfilment of the requirements for the degree of Master of Science (Petroleum Engineering).

Vienna, Austria

Date_____________________

Signed: _____________________________

Karakoz Kozhakhmetova

Approved: ___________________________

Dr. Johannes Pichelbauer Thesis Advisor

Leoben, Austria

Date________________________

________________________________

Univ.-Prof. Dipl.-Geol. Ph.D. Stephan Matthai

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I declare in lieu of oath, that I wrote this thesis and performed the associated research myself, using only literature cited in this volume.

___

Date Karakoz Kozhakhmetova

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ABSTRACT

The Haag field in the Molasse Basin in Upper Austria is a depleted dry gas reservoir that was converted to underground gas storage. Three horizontal wells have been drilled to implement a gas storage facility. During their development many areas are subject to uncertainties. This work investigates the overall range of uncertainty in well performance prediction.

Well performance is calculated by semi-analytical and numerical approaches. For the semi- analytical approach a software package of Petroleum Experts, PROSPER, is used. The inflow performance of a well is calculated based on a specified well model. The three models applied are Kuchuk and Goode, Goode and Wilkinson, and Babu and Odeh. Further work is then based on Kuchuk and Goode model.

The numerical approach is based on the finite difference method, and the simulation software of Schlumberger, ECLIPSE. The simulation model used is the history matched model of the gas storage facility.

Inflow performance curves for different scenarios were determined by these two approaches and the results of the two approaches are then compared. The inflow performance curves calculated semi-analytically are considered to be more realistic, because they are based on models specifically developed for horizontal wells. Therefore, these inflow performance curves are used as reference curves.

The calculations indicate that the inflow performance calculated numerically is too optimistic compared to the semi-analytical approach. Thus, the inflow performance of horizontal wells, calculated numerically, needs to be corrected for future simulation forecasts. However, it is not possible to determine a general correction factor. Performance must be evaluated for each well individually. For this task it is recommended to construct semi-analytically inflow performance models.

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KURZFASSUNG

Das ausgeförderte Gasfeld Haag liegt im Molasse Becken in Oberösterreich und wurde in einen Untertage Erdgasspeicher umgewandelt. Zu diesem Zweck wurden drei horizontale Speicherbohrungen abgeteuft. Bei der Entwicklung eines Untertage Gasspeichers existieren verschiedene Bereiche in denen man mit Unsicherheiten in der Bestimmung der notwendigen Daten und Parameter konfrontiert ist. Diese Arbeit behandelt die Unsicherheiten im Bereich der Berechnungen der Sondenkapazitäten.

Die Sondenkapazitäten wurden mit semi-analytischen und numerischen Ansätzen berechnet.

Für den semi-analytischen Ansatz wurde das Software Packet von Petroleum Experts, PROSPER, verwendet. Die Berechnungen basieren auf verschiedenen Horizontalsondenmodellen, die verwendeten drei Modelle sind von Kuchuk & Goode, Goode

& Wilkinson, and Babu & Odeh. Für die weiteren Berechnungen in dieser Arbeit wurde das Modell von Kuchuk & Goode verwendet.

Der numerische Ansatz basiert auf der Finite Differenz Methode, die Simulationssoftware von Schlumberger, ECLIPSE, wurde hierfür benutzt. Das verwendete Simulationsmodell ist das an den historischen Daten geeichte Modell des Gasspeichers.

Mit diesen zwei Ansätzen wurden „Inflow Performance“ Kurven (IPR Kurven) für unterschiedliche Szenarien ermittelt und die Ergebnisse verglichen. Da der semi-analytisch Ansatz auf Modellen, entwickelt speziell für Horizontalsonden basiert, wurden diese IPR Kurven als Referenzwerte verwendet.

Die Auswertung hat gezeigt, dass die numerisch berechneten Sondenkapazitäten der horizontalen Speichersonden zu optimistisch waren. Daher müssen diese Werte korrigiert werden um zuverlässige Modelle für Vorhersagen zu erhalten. Es ist jedoch nicht möglich, einen allgemeinen Korrekturfaktor zu finden, deshalb muss dieser Faktor für jede Sonde individuell bestimmt werden. Es wird daher empfohlen jeweils semi-analytische IPR Modelle zu erstellen um den notwendigen Korrekturfaktor für die numerischen Berechnungen bestimmen zu können.

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LIST OF FIGURES

Figure 2-1: RAG Concessions on a Geological Map of Germany and Austria (after RAG)... 3

Figure 2-2: Location of Haag Field in RAG’s Austrian Concession (after RAG)... 3

Figure 2-3: Geological cross-section through the Molasse Basin (after RAG) ... 4

Figure 3-1: Interpreted 3-D reflections seismic section showing the geological setting of the Haag Field at the northern Slope of the Molasse Basin (after RAG)... 7

Figure 3-2: Static model with the Zone 1... 8

Figure 3-3: Top model... 8

Figure 3-4: Base model ... 9

Figure 3-5: Histogram of facies distribution ... 9

Figure 3-6: Sand and shale distribution in the reservoir ... 10

Figure 3-7: Permeability vs. Porosity... 11

Figure 4-1: Petroleum Experts IPR Relative Permeabilities model⁶... 14

Figure 4-2: Comparison of IPR models for HAAG-001... 15

Figure 4-5: Comparison of IPR models for HAAG-001 in injection phase... 18

Figure 4-6: Comparison of IPR models for HAAG-002 for the injection phase ... 19

Figure 4-7: Comparison of IPR models for HAAG-003 for the injection phase ... 20

Figure 4-8: Horizontal-well model⁸... 23

Figure 4-9: Schematic of partially open horizontal well⁹... 24

Figure 4-10: Drainage volume of horizontal well⁹... 26

Figure 4-11: Comparison of IPR model for HGSP-001 at pres=91 [bara]... 31

Figure 4-14: Comparison of IPR curves for HGSP-001 with two different reservoir models. 33 Figure 4-15: Comparison of IPR models for HGSP-001 ... 33

Figure 4-16: Skin influence with Kuchuk & Goode model ... 35

Figure 4-17: Comparison of two models with skin value 0 ... 35

Figure 4-18: Comparison of IPR curves for HGSP-001 with different k at pres=91 [bara]... 36

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Figure 4-22: The influence of permeability on IPR curve at pres=55 [bara] ... 38

Figure 4-23: The influence of permeability on IPR curve at pres=43 [bara] ... 39

Figure 4-24: The impact of different effective well length on IPR curve at pres=91 [bara] ... 40

Figure 5-1: Linear relationship of modified permeability and porosity... 43

Figure 5-2: Permeability-porosity correlations ... 43

Figure 5-3: Pressure history match, HAAG-001... 44

Figure 5-4: Gas production rate history match, HAAG-001... 45

Figure 5-9: Withdrawal profile for Haag underground storage facility ... 48

Figure 5-10: Withdrawal profile vs. time... 48

Figure 5-11: Influence of different skin values at pres=91 [bara] ... 50

Figure 6-1: Comparison of results at pres=91 [bara] for HGSP-001... 53

Figure 6-4: Comparison of the PROSPER IPR curve with corrected curve from ECLIPSE .. 55

Figure 6-5: Comparison of the corrected curve at pres=55 [bara]... 55

Figure 6-6: Comparison of the corrected curve at pres=55 [bara]... 56

Figure 6-7: IPR without productivity multiplier at pres=91 [bara] for HGSP-002 ... 57

Figure 6-8: IPR with productivity multiplier at pres=91 [bara] for HGSP-002 ... 57

Figure 6-9: IPR without productivity multiplier at pres=91 [bara] for HGSP-003 ... 58

Figure 6-10: IPR with productivity multiplier at pres=91 [bara] for HGSP-003... 58

Figure 7-1: Withdrawal profiles with and without productivity multipliers... 61

Figure 8-1: A schematic diagram of pressure loss along the well length¹²... 62

Figure 8-2: Viscosity vs. pressure ... 65

Figure 8-3: Density vs. pressure... 65

Figure 8-4: Velocity in the tubing vs. pressure ... 66

Figure 8-5: Reynolds number (tubing) vs. pressure... 66

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Figure 8-6: Reynolds number (perforation) vs. pressure ... 70

Figure 8-7: Velocity in the perforation vs. pressure... 70

Figure A- 1: Standing-Katz Z-factor chart¹⁴... 75

Figure A- 2: Pressure distribution in the Haag reservoir – 1983 ... 76

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LIST OF TABLES

Table 2-1: Summary of reservoir characteristic in Haag field ... 2

Table 3-1: Completion Intervals for Haag vertical wells... 12

Table 3-2: Completion Intervals for Haag horizontal wells... 12

Table 4-1: Input parameters in both models at pres=91 [bara] and T= 42°C ... 15

Table 4-4: Input parameters in both models at pres=45 [bara]... 19

Table 4-7: Input data ... 30

Table 6-1: Comparable input data used in ECLIPSE... 52

Table 6-2: Input data for PROSPER ... 52

Table 8-1: Perforation data of HGSP-001... 68

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ACKNOWLEDGMENTS

I would like to express my sincere appreciation to the Rohöl – Aufsuchungs AG and its employees for their support of this thesis. I would specifically like to thank my mentor, Dr.

Johannes Pichelbauer for his valuable suggestions and assistance, and lots of patience. I must also acknowledge MSc. Bernhard Griess, whose expertise, understanding and patience, added considerably to my graduate experience. Particular thanks to Dr. Ralph Hinsch and MSc.

Wolfdietrich Jilg for taking the time to explain the geology of the field.

Further, I would like to extend my thanks to Professor Stephan Matthai, for his advice and guidance in writing this thesis.

I’m very grateful to Mr. Arnold Wahl for providing me this great and unique opportunity and financial support to get an academic degree in Austria.

I would like to express my deepest gratitude to my parents and my American family, Bidgoods, for their incredible support and love in all good and hard times.

Very special thanks go out to my friend, Pavel, who supported me fully in this process and has been an endless source of encouragement throughout the years I have known him.

Finally, I would like to thank God.

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1 INTRODUCTION

RAG builds an underground gas storage using the depleted gas reservoir HOF3 in the Haag gas field. Schlumberger DCS and other consulting companies proved the convenience of the Haag field for storage operation by performing integrated reservoir studies. The further detailed design and the development of underground gas storage was done using a dynamic reservoir simulator.

During this kind of work different areas are subject to strong uncertainties in regard of storage development. For example, the determinations of long-term pressure development because of the uncertainty in the aquifer support, the correct modulation of the water-gas contact movement during the storage cycles. Well performance predictions lack relevant historic dynamic data as the potential of storage wells is usually an order of magnitude larger than that of existing production wells for which data exist.

The aim of this work is to evaluate the range of uncertainty in well performance predictions in case of the Haag underground gas storage and to develop recommendations for future gas storage developments.

The subsurface part of the gas storage Haag consists of three horizontal storage wells, drilled in 2008, and three vertical wells, mainly used for observation purposes but also used as back-up storage wells.

Well performance and productivity were calculated by a semi-analytical and numerical approach.

For the semi-analytical approach a software package from Petroleum Experts (IPM- PROSPER) was used. For each well a so called “Integrated Production Model” was constructed, each based on a different well model. IPR curves for various operating conditions were calculated. The impact of changing skin, permeability and effective well length on performance of the storage wells has been evaluated as well.

The numerical approach is based on the finite difference method. The simulation software ECLIPSE from Schlumberger was employed in numerical approach. The dynamic simulation model for the gas storage was used to calculate comparable well performance data by simulating withdrawal scenarios with the same operating conditions as in the analytical case.

The results of the semi-analytical and numerical approach were compared and

recommendations to improve well performance predictions of future simulation models were derived.

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2 FIELD DESCRIPTION

The Haag field is located in one of RAG’s concessions of the Molasse Basin in Upper Austria (See Fig. 2.1, Fig. 2.2). The Molasse Basin is a foreland basin, which, from Oligocene onwards was in compression due to the Alpine Orogeny (See Fig. 2.3). This field was discovered in 1981 by exploration well HAAG-001 and has been extended with the wells HAAG-002 and HAAG-003 in the gas bearing horizon ‘HOF-3’ close to the Hall formation.

The depositional environment of the gas bearing sands is of deep marine character. The reservoirs are part of a turbiditic channel belt which was fed from different source points. The dominant sediment transport direction in this particular reservoir was from west to east along the northern flank of the Northern Calcareous Alps. The reservoir comprises channel deposits which pinch out and are flanked by shale as well as sloping fan deposits that pinch out towards the north. HAAG-001 has been drilled through 5.0 m (MD) net gas sands, HAAG- 002 through 12 m (MD) and HAAG-003 through 5.9 m (MD) net gas in the HOF-3 horizon.

The average porosity is 30 % and average permeability is in the range of 250 mD. The field has an East-West trend with dimensions of 1500 m and 3000 m in the N-S and E-W directions respectively.

Proven GIIP is 420 Mio. m³(Vn) and the estimated ultimate recovery is 405.5 Mio. m³(Vn).

Production histories and previous studies i.e. simulations of the reservoir have shown negligible connate water in the system. However, HAAG-002 has a secondary gas-water contact at -460.8 m TVDSS.

Table 2-1: Summary of reservoir characteristic in Haag field

GIIP proved [Mio.m³(Vn)] 420 Ultimate Recovery [Mio.m³(Vn)] 405,5

Reservoir Depth [m] 985

Initial Reservoir Pressure [bara] 91 Net Thickness [m] 5 - 12

Reservoir N/S [m] 1500

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Figure 2-1: RAG Concessions on a Geological Map of Germany and Austria (after RAG)

Figure 2-2: Location of Haag Field in RAG’s Austrian Concession (after RAG)

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Figure 2-3: Geological cross-section through the Molasse Basin (after RAG)

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3 FIELD DATA

The Haag dry gas reservoir started producing in mid-1983 through HAAG-001. In 1986 two more vertical wells, HAAG-002 and HAAG-003, were drilled. In 1993 HAAG-001 reached peak production of about 107103 [Sm³/d], while HAAG-002 and HAAG-003 peak production of 75x10³ [m³(Vn)/d] and 85x10³ [m³(Vn)/d)] was reached in 1991 and 1994 respectively. At the end of February 2005, the production from all three wells was below 14x10³ [m³(Vn)/d].

The surface limit for production was about 190x10³ [m³(Vn)], which was attained in mid- 1994.

It was decided to convert this depleted field to gas storage. Three horizontal wells were drilled to serve as injection/withdrawal wells. The main reason for deciding for horizontal wells was the relative thin thickness of the reservoir. It is difficult to drain large volumes using vertical wells since the contact area is small. Horizontal wells provide an alternative to achieve long penetration lengths in the formation. Another reason would also be the high permeability of the reservoir. In high-permeability gas reservoirs, wellbore turbulence limits the deliverability of a vertical well. To reduce turbulence near the wellbore, the only alternative is to reduce the gas velocity around the wellbore. This can be partly achieved by fracturing a vertical well.

However, fracturing is not very effective in a high-permeability reservoir, because proppants themselves have a limited flow capacity, which may be comparable to that of the reservoir rock. The most effective way to reduce gas velocity around the wellbore is to reduce the amount of gas production per unit well length. This can be accomplished by using horizontal wells. The long wells may produce less gas per unit well length than a vertical well, but total horizontal-well production can be higher than for a vertical well because of the long length.

Thus, horizontal wells provide an excellent method to minimize near-wellbore turbulence, and at the same time, improve total gas production from a well.

3.1 Data Review

3.1.1 Geological Model

The geology department of RAG has constructed a geological model, which forms the basis of the simulation model used in this study.

The reservoir deposits of the Haag Storage are part of the Hall Formation (Burdigalian), which belongs to the deposits of the Northern Alpine Foreland Basin (NAFB), commonly referred to as Molasse Basin².

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The NAFB is a classical foreland basin, fetching the erosional products of the evolving Alpine orogen to the south, starting in upper Eocene times (Nachtman and Wagner, 1987).

Kuhlemann and Kempf² stated “In the Swiss and German Molasse Basin a typical succession of marine to continental shelf deposits characterise the basin fill. In contrast, the eastern Bavarian and Upper Austrian part of the Molasse Basin maintain constant deep marine conditions from Rupelian to Burdigalian”.

Borowski et al.⁴ reported that a major unconformity at the base of the Burdigalian (Base of Hall Group) marks a major erosional event likely corresponding to the end of northward thrusting in of the tectonic units to the south of the basin. After the deposition of the basal beds of the Hall Group, which are deposited only in the central trough of the basin, a system of sedimentary wedges infills the morphological trough left behind by the Base Hall unconformity, prograding from southwest to northeast (See Fig. 3-1). Whether the Hall Group deposits of this system reflect delta sediments with storm reworking or still deep marine deposits is still under debate (Hinsch 2008). The reservoir deposits of the Haag storage belong to this system. The most common interpretation at RAG is that the sandstones represent turbiditic deposits at the toe of the prograding wedges, shed from the south. The Haag area is located at the northern slope of the Hall formation basin. Here, the prograding wedges directly down- and onlaps onto the basal Hall unconformity (See Fig. 3-1). The gas bearing sandstones of the Haag storage are called HOF-3 sands and are usually correlated between the Haag field and the Tratnach field further to the east, where they were encountered water bearing.

In reflection seismic data, the top HOF-3 level is represented by an impedance decrease (trough, red colour in RAG convention). In the area of the Haag storage, this level is characterized by a very high amplitude level, which is a result of the thick sand accumulation.

The former gas trap of the Haag field is mainly a stratigraphic trap, defined by pinch out of the sandstones towards the north, east and west in combination with the deposits dipping towards the south. Parts of the northern pinch out of the Haag field seem to be controlled by east-west striking normal faults, rooting in the Mesozoic deposits and the basement. The top and lateral seal is build by shales of the Hall Group.

The reservoir model was build by using the mapped and depth converted HOF-3 reflector and the amplitude information to constrain pinch outs and reservoir thickness in the field. Well

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Figure 3-1: Interpreted 3-D reflections seismic section showing the geological setting of the Haag Field at the northern Slope of the Molasse Basin (after RAG).

After completion of HGSP-001, 002 and 003 the static model was updated. An additional zone (Zone 1) has been created comprising a suspected initial layer in top-section of HGSP- 001. Zone 1 has a shale (non-reservoir) base. The Figure 3-2 illustrates the updated static model with the Zone 1. The next following figures show the top and base model. The facies modelling in Petrel was used for distribution of reservoir heterogeneity. The properties from upscaled well logs were used for distributing the reservoir facies by using a stochastic method.

The main reservoir, Zone 2, has 72 % sand (reservoir) and 28 % shale (non-reservoir). The quality of the facies distribution in the main reservoir is shown in the histogram table. The percentages of reservoir, upscaled cells and well logs are well matched (see Fig. 3-5).

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Figure 3-2: Static model with the Zone 1

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Figure 3-4: Base model

Figure 3-5: Histogram of facies distribution

0=Res 1=NonRes

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The figure below depicts the overall distribution of reservoir and non-reservoir in the Haag field.

Figure 3-6: Sand and shale distribution in the reservoir

3.1.2 Petrophysical Data

Petrophysical properties were obtained from available logs of wells in the Haag reservoir. The properties which were input to the model were based on the results of petrophysical analysis performed by Schlumberger.

The porosity-permeability relationship is plotted in the following figure. This correlation is analogous to the porosity-permeability correlation of the neighbor field Puchkirchen located about 35 km away from the Haag field.

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0 200 400 600 800 1000 1200 1400 1600 1800

0 0.1 0.2 0.3 0.4

porosity [fraction]

k [md]

Figure 3-7: Permeability vs. Porosity

3.1.3 Initial Data

Initial pressure at datum depth of 411 m was 91 bars and initial temperature was 43 °C. The initial gas-water contact (GWC) was at 465 m TVDSS, which was defined from the observed GWC in well logs of HAAG-002.

3.1.4 SCAL Data

Relative Permeability curves were calculated using the Corey gas-water correlation method (see Appendix A). Capillary pressure curves were obtained on the basis of log data.

3.1.5 PVT Data

The Haag reservoir fluid analysis report indicates about 99 % of methane. Therefore, a specific gravity of 0.562 was used for calculations. Water salinity is 15000 ppm.

The Z-factor was calculated by using Standing and Katz method. The formation volume factor was computed with Z-factor correlation. (See Appendix B and C)

3.1.6 Well Data

Completion intervals of vertical and horizontal wells are tabulated below. The HGSP-001 was drilled from July 27^th till 27^th of August in 2008. The well was drilled down to depth of 1933

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[mMD] which is 1033 [mTVDss]. Then the second storage well HGSP-002 was drilled from 30^th of August till 3^rd of October in 2008. HGSP-002 was drilled to final depth of 1900 [mMD]

that is 1037 [mTVDss]. The third storage well was drilled in the fall of the same year, namely from 6^th of October till 11^th of November, down to depth of 1988 [mMD] which is equal to 1034 [mTVDss]. The sequence of completions in the reservoir was built into the Petrel model for each well.

Table 3-1: Completion Intervals for Haag vertical wells

Well Year Completion Interval [m] (MD) Net Perforation [m]

HAAG-001 1983 984 - 987.5 3.5

HAAG-002 1986 1071.3 - 1084.0 4

HAAG-003 1986 1301.5 - 1311.0 9.5

Table 3-2: Completion Intervals for Haag horizontal wells

Well Year Completion Interval [m] (MD) Net Perforation [m]

HGSP-001 2008 1192.46 - 1893.38 504.6

HGSP-002 2008 1094.52 - 1782.41 469.69

HGSP-003 2008 1181.44 - 1865.14 604.8

3.1.7 Production Data

Gas production data versus time of old vertical wells were provided up to March 2005. The production records showed that perforated pay intervals of the wells had produced gas rates of up to 200,000 [m³(Vn)/d]. The wells could have been produced higher rate but there was a limiting surface constraint.

3.1.8 Pressure Data

Reservoir pressure data provided by RAG had been gathered by RAG since the field start.

The data used for estimating the reservoir pressure had been taken mainly from the flowing measurements. The pressure data had already been screened by RAG to eliminate unreliable data.

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4 WELL PERFORMANCE AND PRODUCTIVITY – ANALYTICAL APPROACH

Well performance was examined analytically using the PROSPER software package. Two different models were used for each well and for different well model scenarios.

4.1 Description of reservoir models used for vertical wells

Since there are only production data, but no well test data for the three vertical wells, HAAG- 001, HAAG-002 and HAAG-003 are available, the input data for IPR and VLP calculations were limited, as a result the number of models available in PROSPER was also limited to two models, namely Jones and Petroleum Experts.

Jones (1976)

The Jones equation for gas is a modified form of the Darcy equation which allows for both laminar and turbulent flow pressure drops. The Jones equation can be expressed in the form of:

2 2

2 p bq aq

p_res − _wf = + (4-1)

where b is a laminar flow coefficient and aq is a turbulence coefficient for gas wells. They are calculated from the reservoir properties or can be determined from a multi-rate test⁶. The definitions for a and b can be derived from the equation for radial pseudo-steady state gas flow, which is given as⁷

2 2

18 2

2 3.16 10 1 1

472 . 0 424 ln

.

1 q

r h r

s ZT r r kh

p ZTq p

e w g

w e wf

res ¸¸¹

¨¨ ·

©

§ −

+ ×

¸¸¹

¨¨ ·

©

§ +

=

−

− βγ

μ _(4-2)

where p_res… average formation pressure [psi]

pwf … Flowing well pressure [psi]

q… Gas flow rate [Scf/d]

re… Well radius [ft]

rw… Well radius [ft]

h… Producing formation thickness [ft]

s… Skin effect excluding turbulence effects [dimensionless]

Z… Dimensionless gas compressibility coefficient T… Reservoir temperature [°R]

μ… Viscosity [cp]

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k… Permeability [md]

β… Turbulence factor [ft^-1] γg… Gas gravity

The darcy term is

¸¸¹

¨¨ ·

©

§ +

= s

r r kh

b ZT

w

472 e

. 0 424 ln

.

1 μ _(4-3)

and, the term re

1 can be neglected since it is usually very small, then a is

w g

r h

a ₂ ZT

10 18

16 .

3 × ⁻ βγ

= ^(4-4)

Petroleum Experts

The Petroleum Experts inflow option for gas and condensate, in PROSPER, uses a multi- phase pseudo pressure function to allow for changing gas and condensate saturations around the wellbore. It assumes that no condensate banking occurs and that all the condensate that drops out is produced. Transient effects on productivity index are accounted for.

Petroleum Experts offers several choices in terms of defining permeability. User can define either effective permeability or total permeability at connate water saturation. In case of defining total permeability, the effective permeability will be calculated depending on the given connate water saturation. The following diagram illustrates how PROSPER treats effective and absolute permeabilities:

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4.1.1 Comparison of the models for the three vertical wells in production phase

The highest production rate out of these three vertical wells was between 2500 – 4300 [m³(Vn)/h]. Rates within the practical range of 0 – 10000 [m³(Vn)/h] were used for the comparison of models.

IPR curves for HAAG-001

The Fig. 4-2 illustrates the IPR curves for HAAG-001 using the Jones (1976) equation and Petroleum Experts. The input parameters for both models are tabulated in the following table:

Table 4-1: Input parameters in both models at pres=91 [bara] and T= 42°C

Parameters Value Reservoir permeability 150 [md]

Reservoir thickness 5.1 [m]

Skin 8.4

Wellbore radius 4.25 [inches]

50 55 60 65 70 75 80 85 90

0 2000 4000 6000 8000 10000

q [m³(Vn)/h]

p [bara]

Jones

Petroleum Experts

Figure 4-2: Comparison of IPR models for HAAG-001

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IPR curves for HAAG-002

The Fig. 4-3 illustrate the comparison IPR curves for HAAG-002 using the Jones (1976) equation and Petroleum Experts. The input parameters for both models are tabulated in Table 4-2.

Table 4-2: Input parameters in both models at pres=91 [bara] and T= 42°C Parameters Value

Reservoir permeability 150 [md]

Skin 17

76 78 80 82 84 86 88 90 92

0 2000 4000 6000 8000 10000

q [m³(Vn)/h]

p [bara]

Jones

Petroleum Experts

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IPR curves for HAAG-003

The following figure illustrates the IPR curves for HAAG-003 using the Jones (1976) equation and Petroleum Experts. The input parameters for both models are tabulated in the table below.

Table 4-3: Input parameters in both models at pres=91 [bara] and T= 42°C Parameters Value

Skin 17.5

76 78 80 82 84 86 88 90 92

0 2000 4000 6000 8000 10000

q [m³(Vn)/h]

p [bara]

Jones

Petroleum Experts

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4.1.2 Discussion of results for vertical wells in production phase

In general, both models deliver approximately same AOFs for each well, and the trend of both IPR models are similar. There is a slight difference to see between the both IPR models in regions, which most likely will not be achieved in practical implementation.

The Petroleum Experts IPR allows for the reduction in effective permeability resulting from liquid production in gas and condensate wells, i.e. it takes liquid production into account. If a reservoir has liquid production, then Petroleum Experts delivers more accurate IPR curve than the Jones (1976) equation.

4.1.3 Comparison of the models for the three vertical wells in injection phase

The Haag field was completely depleted, and pressure build up was necessary to be able to drill the three horizontal storage wells. Pressure build up was performed starting with July 2007 until September 2009 using the three vertical wells, HAAG-001, HAAG-002 and HAAG-003. The same models were applied for building the injection IPR curves for the vertical wells.

IPR curves for HAAG-001

In the following figure the injection IPR curves built by using Jones (1976) and Petroleum Experts models are compared.

30 40 50 60 70 80 90 100 110

p [bara] ^Jones

Petroleum Experts

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Table 4-4: Input parameters in both models at pres=45 [bara]

Drainage area 472548 [m²]

Perforation interval 3.5 [m]

Porosity 0.3 fraction

Input data

IPR curves for HAAG-002

In the figure below the injection IPR curves calculated with Jones (1976) and Petroleum Experts models are compared:

30 40 50 60 70 80 90

0 5000 10000 15000

q [m³(Vn)/h]

p [bara] ^Jones

Petroleum Experts

Figure 4-6: Comparison of IPR models for HAAG-002 for the injection phase

Table 4-5: Input parameters in both models at pres=45 [bara]

Perforation interval 4 [m]

Input data

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IPR curves for HAAG-003

The Fig. 4-7 depicts the comparison of two injection IPR curves constructed using Jones and Petroleum Experts models.

30 40 50 60 70 80 90

0 5000 10000 15000

q [m³(Vn)/h]

p [bara]

Jones

Petroleum Experts

Figure 4-7: Comparison of IPR models for HAAG-003 for the injection phase Table 4-6: Input parameters in both models at pres=45 [bara]

Perforation interval 9.5 [m]

Input data

4.1.4 Discussion of results for vertical wells in injection phase

For HAAG-001 the Jones follows almost a linear trend compared to Petroleum Experts, which follows the exponential trend. They intersect at a rate of about 8300 [m³(Vn)/h]. In case of HAAG-002 and HAAG-003 the two models show same trend up to 5000 [m³(Vn)/h] rate.

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same. To compare the models we need to suppose a scope within which results are considered to be equal. Thus this scope permits a practical comparison of results.

4.2 Inflow Performance of Horizontal Wells

As around the world interest in drilling horizontal wells to increase productivity has grown, several methods to calculate pseudo-steady productivities of horizontal wells for single-phase flow have been introduced in the literature. Unfortunately, most of them contain unacceptable simplifying assumptions. In this work three types of these methods are used to construct inflow performance curves in semi-analytical approach with PROSPER. They are less

restrictive than other methods appeared in the literature. These three treatments are Kuchuk &

Goode, Goode & Wilkinson, and Babu & Odeh. In all these methods, the reservoir is assumed to be bounded in all directions and the horizontal well is located arbitrarily within a

rectangular bounded drainage area.

4.2.1 Kuchuk and Goode method (1991)

The inflow performance of a well is related to the pseudo-steady-state or steady-state behavior.

For a reservoir with no-flow boundaries, the difference between the average pressure of the reservoir and the wellbore pressure draws near a constant value, which is called the pseudo- steady-state pressure. This applies for a reservoir with no-flow boundaries. If the reservoir is bounded above and/or below by a constant-pressure boundary (e.g., gas cap or strong aquifer) then at long times, the difference between the pressure at the boundary and the pressure in the well will become a constant, called the steady-state pressure. When the pseudo-steady- or steady-state is normalized with respect to the stabilized well flow rate, it provides a measure of the pressure drawdown required to flow a unit volume per unit time. The dimensionless pseudo-state pressure,p_wD, for the no flow case is defined as

(

⁽ ⁾ ⁽ ⁾

)

2 p t p t

q h

p_wD = k^H − _w μ

π _(4-5)

where p(t)= average reservoir pressure at time t p_w(t)= pressure at the wellbore

k_H = k_xk_y

For the constant pressure boundary case,

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(

⁽ ⁾

)

2 p p t

q h

p_wD = k^H _e − _w μ

π _(4-6)

where p_e= pressure at the constant-pressure boundary.

The inflow performance is often expressed as

) 10 (

08 .

7 ³ _*

m wD o

H

S p B

h J k

× +

= ⁻

μ In oilfield units – [STB/d-psi]) (4-7)

In this formula S_m^*is defined as

m z x

m S

k k L

S h ¸¸ ⋅

¹

¨¨ ·

©

=§

2 / 1

*

2 ^(4-8)

whereS_m, the usual van Everdingen mechanical skin, is related to the pressure drop across the skin region, Δp_s, by

s z y

m p

q k k

S L ¸¸Δ

¹

·

¨¨

©

=§

μ π 1/2

2 (4-9)

This is necessary because p_wD has been made dimensionless with respect to the formation thickness, not the length of the well over which the pressure drop owing to skin occurs.

As already mentioned above, most of the inflow-performance formulas for horizontal wells presented in the literature make certain limiting assumptions about the well. Particularly, the well length has been assumed to be long compared with the formation thickness and to be short compared with the dimensions of the drainage area; and the well is required to be in the center of the drainage volume. Goode, P.A. and Kuchuk, F. J.⁸ have presented formulas for evaluating the inflow performance of a horizontal well in a rectangular drainage region of uniform thickness and do not need the assumptions mentioned above. The well is assumed to be parallel to the x direction and it can be placed anywhere within the drainage volume, as shown in Fig. 4-8, which gives all the relevant parameters. All boundaries are closed to flow (no flow) except the top boundary, which may be a no-flow or constant-pressure boundary.

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Figure 4-8: Horizontal-well model⁸

The only other assumption required is that, if the well is not long compared to with the scaled reservoir thickness

(

^h ^k^x^/^k^z

)

, the distance from the well to any lateral boundary must be large relative to the distance from the well to the top and bottom boundaries. In practice this is not an unduly restrictive assumption, unless the vertical permeability is extremely low, which in any event would make the reservoir a poor candidate for development with horizontal wells.

The pseudo-steady-state pressure is given by

( )

zD

x n x y

w y w y

x x

y

wD S

n L

L L

y L y k

k L

p L ¸¸+ Ξ + +

¹

·

¨¨

©

§ − +

=

¦

^∞

= ξ

π

π 1 ²1

²

² 2 3

2 1

2 1 / 1

2 2

2

(4-10)

where

°¿

°¾

½

°¯

°®

¸

¹

¨ ·

©

§ − +

»+

¼

« º

¬

ª ¸

¹

¨ ·

©

− §

= ²

² 3

sin 1 '2

2 ₁_/₂ ln ₁_/₂ h

z h z L

h k k h

z h

r k

k L

S h ^w ^w

z x w

w z

x zD

π

π (4-11a)

¸¸

¹

·

¨¨

©

§ +

¸¹

¨ ·

©

=§

y z w

w k

k

r r 1

' 2 (4-11b)

y w w y y

L y y L L

e

e e

e

α α α α

ξ −

+

= + ⁻

1

2 ⁽ ⁾

(4-11c)

y x

x k

k L

nπ

α ⁼⁻² (4-11d)

And ¸¸¹

¨¨ ·

©

¸¸ §

¹

¨¨ ·

©

= § Ξ

x w x

x L

n x L

n L

n^sin π ^cos π

1 ₁_/₂

(4-11e) Although Eq. 4-10 contains an infinite series, it is not difficult to calculate because the series converges rapidly.

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4.2.2 Goode and Wilkinson method (1991)

This method expands the work of Kuchuk and Goode⁸ to include the effects of having only a portion of the well open. The same horizontal well model as in Kuchuk & Goode is

considered. The well produces through n_p open intervals, with segment i of length 2 L_i centered atx_i (Fig. 4-9).

Figure 4-9: Schematic of partially open horizontal well⁹

Goode and Wilkinson⁹ consider the inflow pressure as a sum of two pressure drops, namely a 2D fracture contribution and a 3D well contribution:

zD xyD

ID p S

p = + (4-12)

The first part, p_xyD, is the dimensionless pressure in the x and y plane resulting from considering the well as a set of fractures that fully penetrate the formation:

2

1 1

sin

³ cos

²

² 2

²

² 3

2 1

¸¸¹

·

¨¨©

§ ×

+ Ξ

¸¸

¹

·

¨¨

©

§ − +

=

¦ ¦

=

∞

= np

i x

i n

n p

x y

w y w y

x x

y

xyD L

L n L

x n n

L L L

y L y k

k L

p L π π

π

π (4-13)

where

{ ( ) ⁽ ⁾ [ ( ) ] }

( )

[

ⁿ ^y

]

w y n w

n y

n nL y L y L

α α α

α exp 2 exp 2 1 exp 2

2 exp

1+ − + − + − − − −

=

Ξ (4-14)

y x x

n k

k L nπ

α = (4-15)

And L is the total open half-length of the well,

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The second term,S_zD, is the geometric skin that results because the well does not fully penetrate the formation and flow must converge near the well:

h z F k

h z h z k

k L

h n h z h

r k

k L

S h ^w

k w k

w w z

x p w p

w z

x p

zD π π ^² ₂ ₍β ₎_cos_² π

3 sin 1

' ln 2

2 1

*

2

¦

^∞

=

»+

»¼ º

««

¬

ª ¸

¹

¨ ·

©

§ − +

¸−

¹

¨ ·

©

− §

=

(4-17)

where

w y

w z r

k

r k ¸¸

¹

·

¨¨

©

§ +

= 1

2

' 1 (4-18)

x z

k k

k h

k

²

² π²

β = ^(4-19)

and the function F_w^*is defined as

( ) ³ ¦ ( ) ¦ ( )

= <

∞

»¼

« º

¬

ª − + − − ×

−

= ∂ ^p

n

i

j i

i j

i j i

p

w uL ux x uL uL

u u u F L

1

* exp 2 4 exp sinh sinh

² 2

1

² ² 1

β β

β

(4-20) These formulas were obtained with the uniform-flux, line-source solution and by averaging the pressure along the well length.

4.2.3 Babu and Odeh method (1987)

Babu and Odeh¹⁰ derived the following equation for horizontal well pseudo-steady state flow potential, i.e. productivity of a horizontal well:

( )

¸¸¹

·

¨¨©

§ + − +

−

= ×

−

R H

w

wf av x z

S r C

B A

p p k k q b

75 . 0 ln

ln 10 08 .

7 ³

μ

(4-21)

where

=

q Flow rate, [STB/day]

=

b Width of drainage volume, [ft]

z =

x k

k , Permeability in the x and z-directions, respectively, [md]

av =

p Average pressure in the drainage volume of the well, [psi]

wf =

p Average flowing bottom hole pressure of the well, [psi]

=

B Formation volume factor, [RB/STB]

μ =Viscosity, [cp]

H =

C Geometric factor, dimensionless

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=

A Drainage area = ah, [ft²]

w =

r Wellbore radius, [ft] and

R =

S Skin due to restricted entry to flow: occurs only when the well length L < b.

SRis a function that depends on the well length. S_R =0when L=b(the fully penetrating case). Eq. 4-21 assumes there is no mechanical skin. If this happens, then S_Rwould become

(

^S^R ⁺^S^f

)

^{, where}^S^fis skin due to damage or improvement around the wellbore.

Figure 4-10: Drainage volume of horizontal well⁹

The above figure depicts the drainage volume of the horizontal well. The coordinates (x0, y1, z0) and (x0, y2, z0) refer to the location of the beginning and the end of the well, respectively.

Since the productivity index (P.I.) is q p

Δ , the P.I. using Eq. 4-18 is defined as

¸¸

¹

·

¨¨

©

§ − +

= ×

−

R w

H

z x

r S A B C

k k I b

P

75 . 0 ln

10 08 . . 7

.

3

μ

(4-22)

These equations above contain two parameters C_H andS_R, which are functions of the aspect ratio, i.e. the relative magnitude of a, b, and h; the values of kx, ky, and kz; and the location of the well. Here, lnC_H is defined as

088 . 1 ln

5 . 180 0

sin

² ln

² 3

28 1 . 6

ln ⁰ ⁰ ⁰ −

»»

¼ º

««

¬

− ª

»¼º

«¬ª °

−

¸¹

¨ ·

©

§ − +

=

x z x

z

H k

k h a h

z a

x a x k

k h

C a (4-23)

Again, x and z are the x and z coordinates of the well.

h b

a

z y

x x0, y1, z0

x₀, y₂, z₀

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Case 1:

z y

x k

h k

b k

a 0.75 0.75

>

≥ and Case 2:

z x

y k

h k

a k

b ≥1.33 >

It is assumed that a and b will be orders of magnitude larger than h so that ¸¸

¹

·

¨¨

©

§ kz

h is always

less than ¸¸

¹

·

¨¨

©

§ kx

a and ¸¸

¹

·

¨¨

©

§ ky

b . If this does not hold, the exact solution shows that there will be

a loss in productivity in drilling a horizontal well instead of vertical well.

Case 1:

As stated previously, SR =0when L = b. If L<b, then PXY

PXYZ

S_R = +

Here, the PXYZ component is due to the degree of penetration, i.e. to the value of L/b, and PXY component is due to the location of the well in the x-y plane. The skin component due to the z-location is negligible and is ignored.

The PXYZ component:

»¼

« º

¬

ª + −

¸¹

¨ ·

©

§ −

= 1 ln 0.25ln 1.05

z x

w k

k r

h L

PXYZ b (4-24)

The PXY component:

¿¾

½

¯®

»

¼

« º

¬

ª ¸

¹

¨ ·

©

§ −

−

¸¹

¨ ·

©

§ +

+

¸¹

¨ ·

©

= §

b L f y

b f L k k Lh PXY b

y z

2 4 2

5 4 . 2 0

²

2 ₀ ₀

(4-25) where

»»

¼ º

««

¬

ª ¸

¹

¨ ·

©

− §

¸¹

¨ ·

¸¹

¨ ·

©

−§

=

¸¹

¨ ·

©

§ ²

137 2 . 2 0 ln 145 . 2 0

2 b

L b

f L (4-26)

The evaluation of ¸

¹

¨ ·

©

§ +

b L f y

2 4 ₀

and ¸

¹

¨ ·

©

§ −

b L f y

2 4 ₀

depends on their arguments i.e. ¸

¹

¨ ·

©

§ +

b L y

2 4 ₀

and ¸

¹

¨ ·

©

§ −

b L y

2 4 ₀

. If ¸

¹

¨ ·

©

§ +

b L y

2 4 ₀

or 1

2 4 ₀

≤

¸¹

¨ ·

©

§ −

b L

y , Eq. 4-23 is used. In this case ¸

¹

¨ ·

©

§ b L 2 is

replaced by ¸

¹

¨ ·

©

§ +

b L y

2 4 ₀

and/or ¸

¹

¨ ·

©

§ −

b L y

2 4 ₀

. On the other hand, if the argument is > 1 then for

2 1 4 ₀

>

¸¹

¨ ·

©

§ +

b L

y , one computes:

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»»

¼ º

««

¬

ª ¸

¹

¨ ·

©

§ − +

−

¸¹

¨ ·

©

§ − +

+

¸¹

¨ ·

©

§ − +

=

¸¹

¨ ·

©

§ ₀ + ₀ ₀ ₀ ²

2 2 4 137 . 2 0

2 4 ln 145 . 2 0

2 4 2

4

b L y b

L y b

L

f y (4-27)

and for 1

2 4 ₀

>

¸¹

¨ ·

©

§ −

b L

y ,

»»

¼ º

««

¬

ª ¸

¹

¨ ·

©

§ − −

−

¸¹

¨ ·

©

§ − −

+

¸¹

¨ ·

©

§ − −

=

¸¹

¨ ·

©

§ 0 − 0 0 0 ²

2 2 4 137 . 2 0

2 4 ln 145 . 2 0

2 4 2

4

b L y b

L y b

L

f y (4-28)

Case 2:

In this case, S_R =PXYZ+PY +PYX

The PXYZ component is calculated by Eq. 4-24.

The PY component:

»¼

« º

¬

ª ¸

¹

¨ ·

©

§ −

+

¸¹

¨ ·

©

§ − +

= 3

24

²

² 3

1

² 28 .

6 ₀ ₀

b L b L b

y b y k

k k ah PY b

y z

x (4-29)

where y₀ is the midpoint coordinate of the well.

The PYX component:

¸¸

¹

·

¨¨

©

§ − +

¸¸

¹

·

¨¨

©

¸§

¹

¨ ·

©

§ −

= ₂

2 0 0

3 1 28

. 1 6

a x a x k

k h

a L

PYX b

x

z (4-30)

The productivity equation of Babu & Odeh was extracted from a very complex and general solution. According to the authors the error in using this simple equation is less than 3 percent, in most, if not all cases of interest. It is applicable for any drainage volume dimensions, for any permeability anisotropy, and for any length and location of the horizontal well.

4.2.4 Conclusions

The difference between the three methods is in their mathematical solution methods and the boundary conditions used. For example, Kuchuk & Goode uses an approximate infinite- conductivity solution where the constant wellbore pressure is estimated by averaging pressure values of the uniform-flux solution along the wellbore length. Because of the well boundary condition assumptions, Kuchuk & Goode generally gives the highest flow rate and Babu &

Odeh gives the lowest rate of the three methods. However, the difference in the calculated

Dynamic Modeling of an Underground Gas Storage Facility, History Matching and Prediction